Method of Deriving Digital Terrain Models from Digital Surface Models

1. A method of deriving a digital terrain model from a digital surface model of an area of interest, comprising: a) dividing the area of interest into a plurality of area portions; b) for each area portion calculating, from the digital surface model, a set of candidate surfaces adapted to represent a ground surface in said area of interest; c) for those area portions having at least two candidate surfaces, estimating a distance of each candidate surface from a digital surface model of the ground surface for that area portion by using a function of a set of geometrical features related to a considered candidate surface, said function being derived from a known relation between each candidate surface and the digital surface model of the ground surface, and selecting, as representative of the ground surface in each said area portion having at least two candidate surfaces, a surface among said candidate surfaces having the smallest estimated distance from said ground surface to act as a local surface model for that area portion; d) for those area portions having only one candidate surface, using that one candidate surface to act as a local surface model for that area portion; and e) merging said local digital terrain models for each portion to obtain the digital terrain model of the area of interest.

2. The method of claim 1 , wherein the area portions of said plurality of area portions are such that each area portion intersects with at least another area portion of said plurality of area portions.

3. The method of claim 2 , comprising selecting, for each point of the area of interest belonging to at least two area portions, a minimum height among heights of the local digital terrain models derived for said area portions at that point of the area of interest.

4. The method of claim 1 , wherein step b) comprises applying a random sample consensus method.

5. The method of claim 1 , wherein step b) comprises: b1) selecting three sample points on the digital surface model; b2) calculating a plane passing through the three selected sample points; b3) determining, in said area of interest, a sub-set of points in the digital surface model, the sub-set of points being a distance from a plane within a predetermined range; b4) determining cardinality of said sub-set of points; and b5) if said cardinality exceeds a predetermined threshold, re-calculating the plane by minimizing said distance for all points of the sub-set; b6) otherwise, if said cardinality is lower than the predetermined threshold, repeating steps b1) to b4).

6. The method of claim 5 , comprising repeating steps b1) to b6) a predetermined number of times.

7. The method of claim 6 , comprising storing said sub-set of points at each repetition of steps b1) to b6).

8. The method of claim 7 , comprising selecting, among the stored sub-set of points, the sub-set of points having the greatest cardinality, wherein the plane associated with the selected sub-set of points defines one of said candidate surfaces.

9. The method of claim 8 , comprising repeating steps from b1) to b6) omitting said selected sub-set of points so as to find at least another one of said candidate surfaces.

10. The method of claim 9 , wherein the steps of storing said sub-set of points, selecting the sub-set of points having the greatest cardinality and repeating steps b1) to b6) omitting said selected sub-set of points are performed in each of said area portions.

11. The method of claim 1 , wherein said set of geometrical features related to the considered candidate surface comprises one or more among: a relative cardinality between a set of points that belong to at least a portion of said area of interest and wherein the distance from the considered candidate surface is within a predetermined range and the set of all the points is within said portion of said area of interest; a resistance to a median filtering of said set of points that belong to at least a portion of said area of interest and wherein the distance from the considered candidate surface is within a predetermined range; and a height of the candidate surface.

12. The method of claim 1 , wherein said function is: F ⁡ ( f ⁡ ( μ m , w ) , θ ) = [ f 1 ⁡ ( μ m , w ) … f L ⁡ ( μ m , w ) 1 ] ⁡ [ θ 1 ⋮ θ L + 1 ] wherein : m denotes the generic candidate surface, w denotes a height derived from the digital surface model, f 1 . . . f L are said geometrical features, and 2 1 . . . , 2 L+1 are parameters.

13. The method of claim 12 , wherein said set of geometrical features related to the considered candidate surface comprises one or more among: a relative cardinality between a set of points that belong to at least a portion of said area of interest and wherein the distance from the considered candidate surface is within a predetermined range and the set of all the points is within said portion of said area of interest; a resistance to a median filtering of said set of points that belong to at least a portion of said area of interest and wherein the distance from the considered candidate surface is within a predetermined range; and a height of the candidate surface, and wherein said function is: F ⁡ ( f , θ ) = ( ∑ r = 1 3 ⁢ f r ⁢ θ r ) + θ 4 wherein f 1 , f 2 and f 3 represent said relative cardinality, said resistance to the median filtering, and said height of the candidate surface.

15. The method of claim 12 , wherein said parameters are derivable from the equation: θ ^ = arg ⁢ ⁢ min θ ⁢ ∑ n = 1 N ⁢ ∑ m = 1 M n ⁢ ( g ⁡ ( μ m n | z n ) - F ⁡ ( f ⁡ ( μ m n , w n ) , θ ) ) 2 wherein N denotes the number of said area portions, M n denotes the number of said candidate surfaces for the n-th area portion, μ m n denotes the m-th candidate surface for the n-th area portion, z n denotes the local digital terrain model for the n-th area portion, and w n denotes the local digital surface model for the n-th area portion.

16. The method of claim 1 , wherein merging comprises combining the local digital terrain models by means of a convex combination.

17. The method of claim 16 , further comprising removing discontinuities in the digital surface model obtained by combining the local digital terrain models.

18. The method of claim 1 , further comprising repeating steps a) to c) for at least two subdivisions of said area of interest area portions different in size.

19. A computer program product comprising a non-transitory computer readable medium having stored therein a computer program adapted to implement, when executed, the method according to claim 1 .

20. A system for deriving a digital terrain model from a digital surface model of an area of interest, comprising: a) means for dividing the area of interest into a plurality of area portions; b) means for calculating, for each area portion, a set of candidate surfaces adapted to represent a ground surface in said area of interest from the digital surface model; c) means for estimating, for those area portions having at least two candidate surfaces, a distance of each candidate surface from a digital surface model of the ground surface for that area portion by using a function of a set of geometrical features related to a considered candidate surface, said function being derived from a known relation between each candidate surface and the digital surface model of the ground surface and selecting, as representative of the ground surface in each said area portion having at least two candidate surfaces, a surface among said candidate surfaces having the smallest estimated distance from said ground surface to act as a local surface model for that area portion; d) means for using, for those area portions having only one candidate surface, that one candidate surface to act as a local surface model for that area portion; and e) means for merging said local digital terrain models for each portion to obtain the digital terrain model of the area of interest.